Question

The distribution of room and board expenses per year at a four-year college is normally distributed with a mean of $5850 and standard deviation of $1125. Random samples of size 20 are drawn from this population and the mean of each sample is determined. Which of the following mean expenses would be considered unusual?

		$5,180
		$6,180
		$6,350
		$7,500

Answer 1

Higher the deviation of the sample mean from the population mean, more likely that the sample mean is unusual. Here, 7500 has the highest deviation from mean.

Let M be the sample mean.

E(M) = 5850, s.d.(M) = = 251.5576

Thus, M ~ N(5850, 251.5576) i.e. (M - 5850)/251.5576 ~ N(0,1)

P(X > 7500) = 1 - P(X 7500) = 1 - P[(X - 5850)/251.5576 (7500 - 5850)/251.5576] = 1 - P[(X - 5850)/251.5576 6.56] = 1 - (6.56) = 1 - 1 = 0 [(.) is the cdf of N(0,1)].

So, 7500 is most unusual.